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Real-linear isometries between certain subspaces of continuous functions

100%

Jamshidi A., Sady F.

Open Mathematics

2013

tom 11

nr 11

2034-2043

In this paper we first consider a real-linear isometry T from a certain subspace A of C(X) (endowed with supremum norm) into C(Y) where X and Y are compact Hausdorff spaces and give a result concerning the description of T whenever A is a uniform algebra on X. The result is improved for the case where T(A) is, in addition, a complex subspace of C(Y). We also give a similar description for the case where A is a function space on X and the range of T is a real subspace of C(Y) satisfying a ceratin separating property. Next similar results are obtained for real-linear isometries between spaces of Lipschitz functions on compact metric spaces endowed with a certain complete norm.

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Closed ideals in algebras of smooth functions

74%

Hanin L. G.

Instytut Matematyczny Polskiej Akademii Nauk

CONTENTS Introduction........................................................................................5 1. Main definitions and basic examples..............................................7 2. Closed ideals in Sobolev algebras...............................................10 2.0. Notation...................................................................................10 2.1. Preliminary observations and results.......................................11 2.2. Closed primary ideals..............................................................13 2.3. Spectral synthesis of ideals.....................................................15 3. Spectral synthesis of ideals in the algebras $C^m Lip φ$............18 4. D-algebras...................................................................................21 5. Zygmund algebras.......................................................................26 5.1. Basic properties.......................................................................26 5.2. Extensions, approximations, and traces...................................32 5.3. Closed primary ideals...............................................................40 5.4. Point derivations......................................................................43 5.5. An extension property and spectral synthesis..........................46 5.6. Proof of Theorem 5.1...............................................................48 Appendix..........................................................................................52 1. Traces of generalized Lipschitz spaces.......................................53 2. Traces of Zygmund spaces.........................................................58 3. Proof of Proposition 5.2.11..........................................................62 References.......................................................................................65

Ograniczanie wyników

1 Open Mathematics

1 Hanin L. G.

1 Jamshidi A.

1 Sady F.

1 2013

1 1997

Wyniki wyszukiwania

Real-linear isometries between certain subspaces of continuous functions

Closed ideals in algebras of smooth functions